Which AI Technique best suited to discovering non-linear relationships in data?
You are mixing up lots of things here. Specifically, you seem to be lacking a basic understanding of artificial neural networks and what they can do (e.g. what type of articifial neural networks are linear classifiers/regressors and which can model non-linear relationships). 

Therefore, I'd take a step back and start with understanding the basics of AI. The go-to book for that is 'Artificial Intelligence: A Modern Approach' by Russel and Norvig. It might be a slower (and more theoretical) start but IMO that is the right approach to actually understand what you are doing.